Solve (4^2+(5x^3+1)+3^4+51)

$$( 4 ^ { 2 } + ( 5 x ^ { 3 } + 1 ) + 3 ^ { 4 } + 51 )$$

Evaluate

$$5x^{3}+149$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16+5x^{3}+1+3^{4}+51$$

Add 16 and 1 to get 17.

$$17+5x^{3}+3^{4}+51$$

Calculate 3 to the power of 4 and get 81.

$$17+5x^{3}+81+51$$

Add 17 and 81 to get 98.

$$98+5x^{3}+51$$

Add 98 and 51 to get 149.

$$149+5x^{3}$$

Differentiate w.r.t. x

$$15x^{2}$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16+5x^{3}+1+3^{4}+51)$$

Add 16 and 1 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17+5x^{3}+3^{4}+51)$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17+5x^{3}+81+51)$$

Add 17 and 81 to get 98.

$$\frac{\mathrm{d}}{\mathrm{d}x}(98+5x^{3}+51)$$

Add 98 and 51 to get 149.

$$\frac{\mathrm{d}}{\mathrm{d}x}(149+5x^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 5x^{3-1}$$

Multiply 3 times 5.

$$15x^{3-1}$$

Subtract 1 from 3.

$$15x^{2}$$